Welcome to Shi-Hao Li's personal homepage

Distinguished Researcher
Department of Mathematics
Sichuan University
Chengdu 610064
China

E-mails: shihao.li at scu dot edu dot cn; lishihao at lsec dot cc dot ac dot cn

Office: Room 218, East Jingguan Building, Wangjiang Campus

Education and Employment

Education

• 2009-2013: Bs.C, Xiamen University
• 2013-2018: Ph.D, Chinese Academy of Science, supervisor: Prof. Xing-Biao Hu

Employment

• 2018-2020: Research Fellow, the University of Melbourne, mentor: Prof. Peter J Forrester.
• 2021-now: Distinguished Researcher, Sichuan University.

Research

Research Interests

• Classical integrable systems (In particular on Toda-type lattices and their algebraic structures)
• Random matrix theory and special functions (hypergeometric function, Meijer G-function and Fox H-function)
• Classical (skew-)orthogonal polynomials in Askey-Wilson scheme
• Integrable numerical algorithms

Accepted papers

Shi-Hao Li, Satoshi Tsujimoto, Ryoto Watanabe and Guo-Fu Yu, Cauchy-Jacobi orthogonal polynomials and the discrete CKP equation, accepted by Lett. Math. Phys., DOI:10.1007/s11005-025-02009-9. [Link]
Claire Gilson, Shi-Hao Li and Ying Shi, Matrix-valued theta-deformed bi-orthogonal polynomials, non-commutative Toda theory and B\"acklund transformation, Nonlinearity, 38 (2025) 065003. [Link]
Yi He, Shi-Hao Li, Jian-Qing Sun, and Yuan-Zi Wang, Applications of quasideterminants to non-commutative multistep ε-algorithm, accepted by Numer. Algo, DOI: 10.1007/s11075-025-02045-5. [Link]
Shi-Hao Li, Ying Shi, Guo-Fu Yu and Jun-Xiao Zhao, Matrix-valued Cauchy bi-orthogonal polynomials and a novel noncommutative integrable lattice, Studies in Applied Mathematics, 154 (2025) e70040. [Link]
Zheng Wang, Shi-Hao Li, Kang-Ya Lu and Jian-Qing Sun, Discrete non-commutative hungry Toda lattice and its application in matrix computation, Numer. Algo., 99 (2025), 1289-1315. [Link]
Shi-Hao Li, Bo-Jian Shen, Guo-Fu Yu and Peter J Forrester, Discrete orthogonal ensemble on the exponential lattices, Adv. Appl. Math., 164 (2025) 102836. [Link]
Bao Wang and Shi-Hao Li, On non-commutative leapfrog map, J. Lond. Math. Soc., 111 (2025), e70063. [Link]
Zong-Jun Yao and Shi-Hao Li, Non-intersecting path explanation for block Pfaffians and applications into skew-orthogonal polynomials, Adv. Appl. Math., 163 (2025), 102803. [Link]
Wei Fu and Shi-Hao Li, Skew-orthogonal polynomials and Pfaff lattice hierarchy associated with an elliptic curve, Int. Math. Res. Not. (IMRN), Vol. 2024 (2024), 8695-8715. [Link]
Shi-Hao Li and Guo-Fu Yu, Christoffel transformations for (partial-)skew-orthogonal polynomials and applications, Adv. Math, 436 (2024), 109398. [Link]
Shi-Hao Li, Bo-Jian Shen, Jie Xiang and Guo-Fu Yu, Multiple skew orthogonal polynomials and 2-component Pfaff lattice hierarchy, Annales Henri Poincaré, 25 (2024), 3333-3370. [Link]
Shi-Hao Li, Matrix Orthogonal Polynomials, non-abelian Toda lattice and Bäcklund transformation, Sci. China Math., 67 (2024), 2071-2090. [Link]
Peter J Forrester, Mario Kieburg, Shi-Hao Li and Jiyuan Zhang, Dip-ramp-plateau for Dyson Brownian motion from the identity on U(N), Prob. Math. Phys., 5 (2024), 321-335. [Link]
Mario Kieburg, Shi-Hao Li, Jiyuan Zhang and Peter J Forrester, Cyclic Pólya Ensembles on the Unitary Matrices and their Spectral Statistics, Constr. Approx., 57 (2023), 1063-1108. [Link]
Peter J Forrester, Shi-Hao Li, Bo-Jian Shen and Guo-Fu Yu, q-Pearson pair and moments in q-deformed ensembles, The Ramanujan J., 60 (2023), 195-235. [Link]
Shi-Hao Li and Guo-Fu Yu, Integrable lattice hierarchies behind Cauchy two-matrix model and Bures ensemble, Nonlinearity, 35 (2022), 5109. (coincide with arXiv:1908.08725.) [Link]
Peter J Forrester and Shi-Hao Li, Rate of convergence at the hard edge for various Pólya ensembles of positive definite matrics, Integral Transforms and Special Functions, 33 (2022), 466-484. [Link]
Shi-Hao Li and Lu Wei, Moments of quantum purity and biorthogonal polynomial recurrence, J. Phys. A, 54 (2021) 445204. [Link]
Peter J Forrester, Shi-Hao Li and Allan K Trinh, Asymptotic correlations with corrections for the circular Jacobi beta-ensemble, J. Approximation Theory, 271 (2021), 105633. [Link]
Bo-Jian Shen, Shi-Hao Li and Guo-Fu Yu, Evaluations of certain Catalan-Hankel Pfaffians via classical skew orthogonal polynomials, J. Phys. A, 54 (2021) 264001. [Link]
Peter J Forrester and Shi-Hao Li, Classical skew orthogonal polynomials in a two-component log gas with charges +1 and +2, Adv. Math., 383 (2021), 107678. [Link]
Xiang-Ke Chang, Shi-Hao Li, Satoshi Tsujimoto and Guo-Fu Yu, Two-parameter generalizations of Cauchy bi-orthogonal polynomials and integrable lattices, J. Nonlinear Sci., 31 (2021), paper 30. [Link]
Bao Wang, Xiang-Ke Chang, Xing-Biao Hu and Shi-Hao Li, Discrete invariant curve flows, orthogonal polynomials and moving frame, Int. Math. Res. Not., 14 (2021), 11050-11092. [Link]
Peter J Forrester and Shi-Hao Li, Fox H-kernel and theta-deformation of the Cauchy two-matrix model and Bures ensemble, Int. Math. Res. Not., 8 (2021), 5791–5824. [Link]
Peter J Forrester and Shi-Hao Li, Classical discrete symplectic ensembles on the linear and exponential lattice: skew orthogonal polynomials and correlation functions, Trans. Amer. Math. Soc., 373 (2020), 665-698. [Link]
Zhi-Lan Wang and Shi-Hao Li, BKP hierarchy and Pfaffian point process, Nucl. Phys. B, 939 (2019) 447-464. [Link]
Chun-Xia Li and Shi-Hao Li, The Cauchy two-matrix model, C-Toda lattice and CKP hierarchy, J. Nonlinear Sci., 29 (2019), 3-27. [Link]
Xiang-Ke Chang, Xing-Biao Hu and Shi-Hao Li, Degasperis-Procesi peakon dynamics and finite Toda lattice of CKP type, Nonlinearity, 31 (2018) 4746-4775.[Link]
Xiang-Ke Chang, Xing-Biao Hu, Shi-Hao Li and Jun-Xiao Zhao, Application of Pfaffian in multipeakons of the Novikov equation and the finite Toda chain of BKP type, Adv. Math., 338 (2018) 1077-1118.[Link]
Xiang-Ke Chang, Yi He, Xing-Biao Hu and Shi-Hao Li, Partial-skew-orthogonal polynomials and related integrable lattices with Pfaffian τ-function, Comm. Math. Phys., 364 (2018) 1069-1119.[Link]
Bao Wang, Xiang-Ke Chang, Xing-Biao Hu and Shi-Hao Li, On moving frames and Toda lattices of BKP and CKP types, J. Phys. A, 51 (2018) 324002.[Link]
Xiang-Ke Chang, Xing-Biao Hu and Shi-Hao Li, Moment modification, multipeakons, and nonisospectral generalizations, J. Diff. Equations, 265 (2018) 3858-3887.[Link]
Xiang-Ke Chang, Yi He, Xing-Biao Hu, Shi-Hao Li, Hon-Wah Tam and Ying-Nan Zhang, Coupled KdV equations, skew orthogonal polynomials, convergence acceleration algorithms and Laurent property, Sci. China Math, 61 (2018) 1063-1078.[Link]
Xiang-Ke Chang, Yi He, Xing-Biao Hu and Shi-Hao Li, A new integrable convergence acceleration algorithm for computing Brezinski-Durbin-Redivo-Zaglia’s sequence transformation via pfaffians, Numerical Algorithms, 78 (2018) 87-106.[Link]
Xing-Biao Hu and Shi-Hao Li, The partition function of Bures ensemble as the τ-function of BKP and DKP hierarchies: continuous and discrete, J. Phys. A, 50 (2017) 285201 (20pp).[Link]

Preprints

• Shi-Hao Li, Shou-Feng Shen, Guo-Fu Yu and Jun-Yang Zhang. A direct method in noncommutative integrable systems. arXiv: 2506.18661. [Link]
• Zheng Wang, Shi-Hao Li, Yi He and Jian-Qing Sun. Discrete fractional Lotka-Volterra system and its application in matrix computation, submitted.
• Shi-Hao Li, Discrete integrable systems and condensation algorithms for Pfaffians, arXiv:2006.06221. [Link]

Other Resources

• Department of Mathematics, Sichuan University